Can you join A to A, B to B, and C to C, using three paths that do not intersect within the disk?
Can you join A to A, B to B, and C to C, using three non-intersecting paths within the disk?
First join the B points (you might as well, all the ways you can join them are equivalent), then the C points (likewise), then the A points.
I consider this a good, though easy, metapuzzle-puzzle pair. I believe the problem statement uses both accidental misdirection – interchanging the phrases "within the disk" and "that do not intersect", and deliberate misdirection – the labelling of the pairs of points with the most difficult pair first. This is easier: "Can you join B to B, C to C, and A to A using three non-intersecting paths within the disk?
This is one of several pages on puzzles and metapuzzles .